Rig a strand with multiple control points?
You should take a look at DanPro's Advanced Tentacle Rigging Series. 

It not only has what you want, he builds it up in real time, moreover while explaining what he does.

https://www.youtube.com/playlist?list=PLizSCQYO0I6OtQ479WlMGZE1ssFk2CIUP

Fair word of warning, the videos run 2h all together and building the actual rig took me another 2.